83 lines
1.8 KiB
Typst
83 lines
1.8 KiB
Typst
#import "@local/handout:0.1.0": *
|
|
#import "@preview/cetz:0.3.1"
|
|
|
|
#show: handout.with(
|
|
title: [Warm-Up: What's an AST?],
|
|
by: "Mark",
|
|
subtitle: "Based on a true story.",
|
|
)
|
|
|
|
#problem()
|
|
Say we have a painting on a string. \
|
|
Hang the painting on two nails so that if either is removed, the painting falls. \
|
|
|
|
#v(2mm)
|
|
You may detach the string as you hang the painting, but it must be re-attached once you're done. \
|
|
#hint[The solution to this problem isn't a "think outside the box" trick, it's a clever wrapping of the string.]
|
|
|
|
|
|
#v(2mm)
|
|
|
|
#align(
|
|
center,
|
|
cetz.canvas({
|
|
import cetz.draw: *
|
|
let s = 2.5
|
|
|
|
|
|
line(
|
|
(0 * s, 1 * s),
|
|
(2 * s, 1 * s),
|
|
(2 * s, 0 * s),
|
|
(0 * s, 0 * s),
|
|
close: true,
|
|
stroke: (thickness: 0.8mm),
|
|
)
|
|
|
|
line(
|
|
(0.1 * s, 1 * s),
|
|
(0.5 * s, 1.5 * s),
|
|
(1.5 * s, 1.5 * s),
|
|
(1.9 * s, 1 * s),
|
|
stroke: (thickness: 0.5mm, dash: "dotted"),
|
|
)
|
|
|
|
circle((0.5 * s, 1.5 * s), radius: 0.04 * s, fill: black, stroke: none)
|
|
circle((1.5 * s, 1.5 * s), radius: 0.04 * s, fill: black, stroke: none)
|
|
|
|
line(
|
|
(0.66 * s, 0.66 * s),
|
|
(0.66 * s, 0.35 * s),
|
|
(0.60 * s, 0.1 * s),
|
|
)
|
|
|
|
line(
|
|
(0.72 * s, 0.1 * s),
|
|
(0.66 * s, 0.35 * s),
|
|
)
|
|
|
|
line(
|
|
(0.66 * s, 0.575 * s),
|
|
(0.6 * s, 0.475 * s),
|
|
(0.525 * s, 0.575 * s),
|
|
)
|
|
|
|
line(
|
|
(0.66 * s, 0.575 * s),
|
|
(0.72 * s, 0.475 * s),
|
|
(0.795 * s, 0.575 * s),
|
|
)
|
|
|
|
circle((0.66 * s, 0.66 * s), radius: 0.07 * s, fill: white)
|
|
}),
|
|
)
|
|
|
|
#solution([
|
|
Say we have a left nail and a right nail. The path of the string is as follows:
|
|
- Start on the left
|
|
- Move over both nails, wrap right nail cw
|
|
- Wrap left nail ccw
|
|
- Wrap right nail ccw
|
|
- Exit downwards, in between both nails
|
|
])
|